The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is

The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2}T} \over {\partial {x^2}}}\,\,$$ is

$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by

A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque $$T$$. If the coefficient of kinetic friction is $$\mu $$, the friction force from the ground on the wheel is